Question: Find $\lim_{x\to 1}\dfrac{2x}{x^2-7x+6}$. Choose 1 answer: Choose 1 answer: (Choice A) A $0$ (Choice B) B $\dfrac{1}{14}$ (Choice C) C $\dfrac{1}{7}$ (Choice D) D The limit doesn't exist
Let's try to find the limit using direct substitution. $\begin{aligned} \lim_{x\to 1}\dfrac{2x}{x^2-7x+6}&=\dfrac{2(1)}{1^2-7(1)+6} \\\\ &=\dfrac{2}{1-7+6} \\\\ &=\dfrac{2}{0} \end{aligned}$ Our expression evaluates to a nonzero number over zero. In such cases, the limit doesn't exist. In conclusion, $\lim_{x\to 1}\dfrac{2x}{x^2-7x+6}$ doesn't exist.